Existence of multiple positive solutions to nonhomogeneous Schrödinger–Poisson system

• DOI: 10.1016/j.amc.2015.02.044
• Publication Date: 2015-03-16T13:47:39Z
• Authors: Qi Zhang; Fuyi Li; Zhanping Liang
• Keywords: Infinity; Schrödinger's cat

In this paper, we consider the existence of multiple solutions to the following nonhomogeneous generalized Schrodinger-Poisson system - Δ u + Ku + q ? f ( u ) = g ( u ) + h ( x ) , in R 3 , - Δ ? = 2 qF ( u ) , in R 3 , where q ? 0 is a parameter, 0 ? h ( x ) = h ( | x | ) ? L 2 ( R 3 ) , and g is asymptotically linear or superliner at infinity. We show that there exists q 0 0 such that the system has at least two positive radial solutions for q ? 0 , q 0 ) .